A knowledge of the thermal properties of biomaterials has long been considered important to researchers and others interested in increasing man's understanding of the nature of materials and their thermal interactions, as well as to designers of equipment and systems in which the thermal characteristics of the materials used therein or operated thereon are of significance. For example, important information concerning biological materials, such as human and animal tissues, can be obtained from knowledge of the thermal properties thereof and of the perfusion characteristics of blood flowing therethrough.
Thus, it is known that biomaterials are capable of heat transfers by virtue of a temperature gradient, such heat transfer capability being especially important in living biomaterials because the state of life thereof, for example, may depend on the maintenance of a specific temperature level. Heat transfer by conduction is usually most important in determining the heat transfer within the biological medium and such heat transfer is best characterized in the steady-state by the thermal conductivity, k, of the medium and in the non-steady state by its thermal diffusivity, .alpha.. Since there is no presently known method of determining k and .alpha. of a biomaterial from a knowledge of some other fundamental property or properties thereof, it is necessary to devise appropriate processes and apparatus to measure k and .alpha. in some appropriate manner.
Furthermore, there has been an increasing utilization, particularly in medical research and clinical laboratories, of processes which require heat transfer through biological materials, such as in cryobiology (e.g., cryosurgery), in tissue and organ preservation, in laser-tissue thermal interactions and in the use of thermal therapy for cancer treatment, for example, all of which require a knowledge of such thermal properties for the intelligent use of these processes. Other procedure which are heat transfer dependent and, thus, require a knowledge of thermal properties include clinical applications of ultrasonic wave energy, microwave energy and laser beam energy in both diagnostic and therapeutic operating modes.
Such processes require more extensive and more reliable information concerning the thermophysical properties of such materials and, in particular, information concerning the thermal conductivities, thermal diffusivities and the flow rates of fluids (perfusion) through the biological medium, which information permits the determination of temperature distributions and heat transfer rates. It is particularly important, for example, to monitor the flow rate of blood through tissue so that flow disturbances can be monitored and corrective action taken in cases where maldistribution of blood flow in a patient would have unfavorable and possibly fatal consequences.
Techniques which have been applied to the measurement to properties of biological materials have included both invasive and non-invasive techniques. General summaries of such techniques and the limitations thereof are presented in the text, Annual Review of Biophysics and Bioengineering, "Theory, Measurement and Application of Thermal Properties of Biomaterials," H. Frederick Bowman et al., pp. 43-80, Vol. 4, 1975 and in the text, Heat Transfer in Medicine and Biology, Vol. 1, Edited by A. Shitzer and R. C. Eberhart, "Estimation of Tissue Blood Flow" H. Frederick Bowman, Chapter 9, pp. 193-229, Plenum Publishing Corp. 1984. Still further background information is contained in U.S. Pat. No. 4,059,982 issued to H. F. Bowman on Nov. 29, 1977 as well as in the description of the invention contained therein.
In accordance with the invention described in the aforesaid Bowman patent, a particular thermal model is developed and a particular implementation of the solution of the heat conduction equations utilizing a thermistor probe is described for providing a realistic representation of the thermal properties of the thermistor bead and the surrounding medium so as to produce an accurate measurement of such properties as thermal conductivity and thermal diffusivity from which other thermal properties and states of flow can be derived. In accordance therewith the thermistor bead of the probe is treated as a distributed thermal mass and the heat conduction equation is solved for both the interior of the bead as well as the region of the medium surrounding it.
The thermistor bead is placed in a medium and the bead and the region of the medium surrounding it assume an initial equilibrium, or reference, temperature. The temperature of the bead is raised to a predetermined level above the equilibrium temperature by applying electrical energy to the bead which thereupon thermally dissipates in the bead and its surrounding medium, thereby raising the temperature of the surrounding medium. If the temperature rise in the bead is to be maintained at the desired level, the electrical energy must be dissipated at a rate which is sufficient to maintain the temperature at the desired level and the electrical power required for such purpose depends on the heat transfer characteristics of the surrounding medium. Thus, if the characteristics of the medium are such as to enhance the heat transfer, a greater number of electrical power will be needed to maintain the desired temperature increment between the reference temperature and the temperature at the desired predetermined level, while, if the characteristics thereof are such as to impede heat transfer, less electrical power will be needed to maintain the temperature increment.
In a biological medium such as human or animal tissue, for example, the heat transfer capability of the medium depends upon the intrinsic thermal conductivity of the medium, the local blood flow rate in the medium and the specific heat of the blood therein, such characteristics contributing to a property which, for convenience, can be referred to as the "effective thermal conductivity" of the medium. Such term can be defined as a measure of the rate at which heat is being removed from the bead by (or transported through) a medium in the presence of fluid flow in the medium. Such property can be contrasted with the "intrinsic thermal conductivity" thereof which can be defined as a measure of the rate at which heat can be removed from the bead for a given temperature gradient by (or transported through) a medium in the absence of any fluid flow therein (e.g., a biologic medium in which no blood flow is present).
The initial reference temperature of the bead and medium is determined and power is applied thereto to raise the mean temperature of the bead to a fixed predetermined level and is maintained at a desired, constant level above the reference temperature.
A data processor is used to calculate both the thermal conductivity and the thermal diffusivity of the medium in accordance with expressions derived from solutions to the transient heat diffusion equations both for the interior of the bead and for the surrounding region of the medium, arrived at by using a thermal model which takes into account the distributed thermal mass of the thermistor bead and the thermal characteristics of the surrounding medium.
The flow rate of a fluid which moves through the medium (e.g., the flow rate of blood through a biologic medium) can be calculated in accordance with an expression also derived from solutions to the heat conduction equations which specifically include blood flow (perfusion) as a variable in such a thermal model representation. In order to utilize the heat conduction equations in such a system, the intrinsic thermal conductivity and thermal diffusivity must be determined under no flow conditions (i.e., in the absence of fluid flow). It is in some cases extremely difficult or substantially impossible to make such measurements in living organisms and it has been found necessary to resort to techniques which provide only approximations to such no flow conditions, so that the values used for the intrinsic conductivity and diffusivity involved produce inaccuracies in the calculations of the effective values thereof and of the perfusion values under flow conditions.
Moreover, it is helpful to provide a system in which the temperature and power characteristics are permitted to be controlled in a more flexible manner than in the invention described in the above Bowman patent which normally requires that the power characteristics be such that the bead volume mean temperature be maintained at a specified value, i.e., the value of V.sub.b be kept substantially constant. Further, while the aforesaid Bowman system permits reasonably accurate measurements of perfusion above certain relatively high perfusion levels, it becomes less accurate at relatively lower perfusion levels.